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Edward J. Gilroy

Publications and source records attributed to Edward J. Gilroy.

8 recordsLinked to original sources
USGS2020

Statistical methods in water resources

This text began as a collection of class notes for a course on applied statistical methods for hydrologists taught at the U.S. Geological Survey (USGS) National Training Center. Course material was formalized and organized into a textbook, first published in 1992 by Elsevier as part of their Studies in Environmental Science series. In 2002, the work was made available online as a USGS report. The text has now been updated as a USGS Techniques and Methods Report. It is intended to be a text in applied statistics for hydrology, environmental science, environmental engineering, geology, or biology that addresses distinctive features of environmental data. For example, water resources data tend to have many variables with a lower bound of zero, tend to be more skewed than data from many other disciplines, commonly contain censored data (less than values), and assumptions that the data are normally distributed are not appropriate. Computer-intensive methods (bootstrapping and permutation tests) now improve upon and replace the dependence on t-intervals, t-tests, and analysis of variance. A new chapter on sampling design addresses questions such as “How many observations do I need?” The chapter also presents distribution-free methods to help plan sampling efforts. The trends chapter has been updated to include the WRTDS (Weighted Regressions on Time, Discharge, and Season) method for analysis of water-quality data. This new version contains updated graphics and updated guidance on the use of statistical techniques. The text utilizes R, a programming language and open-source software environment, for all exercises and most graphics, and the R code used to generate figures and examples is provided for download.

Techniques and Methods↗
USGS2010

Comparison of estimators of standard deviation for hydrologic time series

Unbiasing factors as a function of serial correlation, ρ , and sample size, n for the sample standard deviation of a lag one autoregressive model were generated by random number simulation. Monte Carlo experiments were used to compare the performance of several alternative methods for estimating the standard deviation σ of a lag one autoregressive model in terms of bias, root mean square error, probability of underestimation, and expected opportunity design loss. Three methods provided estimates of σ which were much less biased but had greater mean square errors than the usual estimate of σ: s = (1/( n - 1) ∑ ( x i − x¯ ) 2 ) ½ . The three methods may be briefly characterized as (1) a method using a maximum likelihood estimate of the unbiasing factor, (2) a method using an empirical Bayes estimate of the unbiasing factor, and (3) a robust nonparametric estimate of σ suggested by Quenouille. Because s tends to underestimate σ, its use as an estimate of a model parameter results in a tendency to underdesign. If underdesign losses are considered more serious than overdesign losses, then the choice of one of the less biased methods may be wise.

Water Resources Research↗
USGS2010

Estimating constituent loads

Several recent articles have called attention to the problem of retransformation bias, which can arise when log linear regression models are used to estimate sediment or other constituent loads. In some cases the bias can lead to underestimation of constituent loads by as much as 50%, and several procedures have been suggested for reducing or eliminating it. However, some of the procedures recommended for reducing the bias can actually increase it. This paper compares the bias and variance of three procedures that can be used with log linear regression models: the traditional rating curve estimator, a modified rating curve method, and a minimum variance unbiased estimator (MVUE). Analytical derivations of the bias and efficiency of all three estimators are presented. It is shown that for many conditions the traditional and the modified estimator can provide satisfactory estimates. However, other conditions exist where they have substantial bias and a large mean square error. These conditions commonly occur when sample sizes are small, or when loads are estimated during high-flow conditions. The MVUE, however, is unbiased and always performs nearly as well or better than the rating curve estimator or the modified estimator provided that the hypothesis of the log linear model is correct. Since an efficient unbiased estimator is available, there seems to be no reason to employ biased estimators.

Water Resources Research↗
USGS2007

Methods of Fitting a Straight Line to Data: Examples in Water Resources

Three methods of fitting straight lines to data are described and their purposes are discussed and contrasted in terms of their applicability in various water resources contexts. The three methods are ordinary least squares (OLS), least normal squares (LNS), and the line of organic correlation (OC). In all three methods the parameters are based on moment statistics of the data. When estimation of an individual value is the objective, OLS is the most appropriate. When estimation of many values is the objective and one wants the set of estimates to have the appropriate variance, then OC is most appropriate. When one wishes to describe the relationship between two variables and measurement error is unimportant, then OC is most appropriate. Where the error is important in descriptive problems or in calibration problems, then structural analysis techniques may be most appropriate. Finally, if the problem is one of describing some geographic trajectory, then LNS is most appropriate.

Water Resources Bulletin↗
USGS1999

US Geological Survey nutrient preservation experiment: Experimental design, statistical analysis, and interpretation of analytical results

This report describes the experimental details and interprets results from a study conducted by the U.S. Geological Survey (USGS) in 1992 to assess the effect of different sample-processing treatments on the stability of eight nutrient species in samples of surface-, ground-, and municipal-supply water during storage at 4 degrees Celsius for about 30 days. Over a 7-week period, splits of filtered- and whole-water samples from 15 stations in the continental United States were preserved at collection sites with sulfuric acid (U.S. Environmental Protection Agency protocol), mercury (II) chloride (former U.S. Geological Survey protocol), and ASTM (American Society for Testing and Materials) Type I deionized water (control) and then shipped by overnight express to the USGS National Water Quality Laboratory (NWQL). At the NWQL, the eight nutrient species were determined in splits from each of the 15 stations, typically, within 24 hours of collection and at intervals of 3, 7, 14, 22, and 35 days thereafter. Ammonium, nitrate plus nitrite, nitrite, and orthophosphate were determined only in filtered-water splits. Kjeldahl nitrogen and phosphorus were determined in both filtered-water and whole-water splits. Data on which this report is based, including nutrient concentrations in synthetic reference samples determined concurrently with those in real samples, are extensive (greater than 20,000 determinations) and have been published separately. In addition to confirming the well-documented instability of nitrite in acidified samples, this study also demonstrates that when biota are removed from samples at collection sites by 0.45-micrometer membrane filtration, subsequent preservation with sulfuric acid or mercury (II) provides no statistically significant improvement in nutrient concentration stability during storage at 4 degrees Celsius for 30 days. Biocide preservation had no statistically significant effect on the 30-day stability of phosphorus concentrations in whole-water splits from any of the 15 stations, but did stabilize Kjeldahl nitrogen concentrations in whole-water splits from three data-collection stations where ammonium accounted for at least half of the measured Kjeldahl nitrogen.

Water-Resources Investigations Report↗
USGS1980

Cost effective stream-gaging strategies for the Lower Colorado River basin; the Blythe field office operations

This report describes the theoretical developments and illustrates the applications of techniques that recently have been assembled to analyze the cost-effectiveness of federally funded stream-gaging activities in support of the Colorado River compact and subsequent adjudications. The cost effectiveness of 19 stream gages in terms of minimizing the sum of the variances of the errors of estimation of annual mean discharge is explored by means of a sequential-search optimization scheme. The search is conducted over a set of decision variables that describes the number of times that each gaging route is traveled in a year. A gage route is defined as the most expeditious circuit that is made from a field office to visit one or more stream gages and return to the office. The error variance is defined as a function of the frequency of visits to a gage by using optimal estimation theory. Currently a minimum of 12 visits per year is made to any gage. By changing to a six-visit minimum, the same total error variance can be attained for the 19 stations with a budget of 10% less than the current one. Other strategies are also explored. (USGS)

Open-File Report↗
USGS1974

An assessment of areal and temporal variations in streamflow quality using selected data from the National Stream Quality Accounting Network

Streamflow chemical-quality data and stream-temperature data at 88 stations throughout the United States and Puerto Rico were analyzed to develop and to evaluate methodologies for the general assessment of the variation of the Nation's streamflow-quality conditions in space and over time. The spatial variation is described by the use of sample statistics such as minima, maxima, and means of the variables at each station. The temporal variation is described by using nonparametric statistical testing procedures to assess time trends in the data at each station. Evaluation of the coefficients (mean, amplitude, phase coefficient] derived by harmonic analysis of available daily stream-temperature records indicates adequate depiction of yearly seasonal variability and provides information relative to spatial variation in stream temperatures at most sites. Lowest harmonic amplitudes, which are indicative of little seasonal variability in stream temperature, were observed in Florida, along the eastern Gulf coast, and along the Pacific coast. Greatest annual variations in stream temperature exists in the Souris, Red (of the North), and Missouri River basins. Temporal variations in stream temperature denoted by significant changes (at the 99 percent level of confidence) in annual harmonic coefficients were indicated at 15 of 80 stations used in the evaluation. Trends in stream temperature were found to exist at one or more stations in each of the six following areas: the Atlantic coast above Florida; Florida and the eastern Gulf; the Souris River, Red River of the North, and Missouri River basins; the Texas Gulf and Rio Grande area; the Colorado River basin; and the Pacific coast area. Significant trends (at the 99 percent level of confidence) were found in the long-term streamflow chemical quality record at 15 of 88 stations analyzed. Of these stations, 10 showed an increase in levels of specific conductances while 5- showed a decrease. Trends were indicated for water-quality data from stations located in the following areas: the Atlantic coast above Florida; the Souris River, Red River of the North, and Missouri River basins; the Arkansas and Red River basins; the Texas Gulf and Rio Grande area; the Colorado River basin; and the Pacific coast area.

Open-File Report↗